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Statistica Sinica 21 (2011), 307-329





NUISANCE PARAMETERS, COMPOSITE LIKELIHOODS

AND A PANEL OF GARCH MODELS


Cavit Pakel, Neil Shephard and Kevin Sheppard


University of Oxford


Abstract: We investigate the properties of the composite likelihood (CL) method for ( $%%
T\times N_{T}$) GARCH panels. The defining feature of a GARCH panel with time-series length $T$ is that, while nuisance parameters are allowed to vary across $N_{T}$ series, other parameters of interest are assumed to be common. CL pools information across the panel instead of using information available in a single series only. Simulations and empirical analysis illustrate that when $T$ is reasonably large CL performs well. However, due to the presence of nuisance parameters, CL is subject to the incidental parameter problem for small $%%
T.$



Key words and phrases: ARCH models, composite likelihood, nuisance parameters, panel data.

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